An achromatic lens system is used to bring light rays (referred to as "rays") of two wavelengths to the same focus, for example, rays with wavelengths near the end of the visible spectrum (red and blue). FIG. 1A illustrates a typical achromatic doublet. This Figure shows that the blue (B) and red (R) rays cross the optical axis O.A. at the same location, while the green (G) rays cross the optical axis closer to the doublet. FIG. 1B illustrates a typical ray intercept plot of the achromatic doublet (in three wavelengths). This figure shows the amount of transverse ray error .DELTA.Y, in millimeters, on the vertical axis and the relative entrance pupil height of the ray on the horizontal axis. The entrance pupil is defined as the image of the aperture stop as viewed from object space. Relative entrance pupil height h is the fractional height of the entering ray on the entrance pupil aperture.
More specifically, FIG. 1B shows three curves corresponding to three wavelengths of visible light, green G=0.5876, blue B=0.4861, and red R=0.6563 microns. It can be seen that the red and blue wavelength curves intersect. These intersections occur near the edges of the figure and correspond to the rays passing at the edge of the entrance pupil (maximum relative pupil height, h=.+-.1). This type of chromatic correction is generally recommended and works well for light beams of uniform intensity.
The locations of paraxial foci of the lens system are determined by the slope of these curves at the origin, and it can be seen in FIG. 1B that these slopes are different. Thus, the paraxial foci for different wavelengths are not in the same location in this lens system. It is well known that transverse ray error due to a pure focus shift corresponds to a straight line through the origin of a ray intercept plot. When paraxial rays only are considered, focus shift error is the only possible error. FIG. 1B shows two curves (R and B) with positive slope and one curve (G) with a negative slope. A curve with a positive slope indicates that the paraxial focus for that wavelength is located to the right of the image plane at which the transverse ray error .DELTA.Y is plotted, or farther away from the lens system. A curve with a negative slope indicates that the paraxial focus for that wavelength is located to the left of the image plane, closer to the lens system. Therefore, FIG. 1B indicates that the red and blue paraxial rays focus further from the lens system than the green paraxial rays, and that the blue paraxial rays focus closer to the green paraxial rays than the do the red paraxial rays. This is shown in FIG. 1C, where Rp, Bp and Gp are red, blue and green paraxial rays.
An apochromatic lens system is similar to an achromatic lens system except that it is designed to focus three or more wavelengths to the same location. It is noted that because of the design difficulty and glass costs of correcting three or more wavelengths, most lens systems are achromatic and not apochromatic. However, apochromatic lens systems are well known. Applications for such apochromatic lens systems can be found in telescopes, microscopes, cameras, and some finite conjugate relay systems. Typical chromatic correction for an apochromatic lens system is shown in the ray intercept plots of FIG. 2. This figure illustrates that the rays of all three wavelengths passing through the edge entrance pupil (h=1) have substantially the same height .DELTA.Y at the image plane. This type of chromatic correction works well for multiple wavelength light beams of uniform intensity. FIG. 2 also discloses that the image plane is located at the green paraxial focus, but the red paraxial focus is focused farther from the lens system and the blue paraxial focus is closer to the lens system.
Ideal laser beams have Gaussian intensity profiles and because of this laser beams are often referred to as Gaussian beams. A Gaussian intensity profile is illustrated in FIG. 3A. Focused laser beams do not come to a single point, but form a beam waist (FIG. 3B). A beam waist is a portion of a laser beam that has a smaller cross section than the adjacent areas. Beam waists, like the rest of the laser beams also have Gaussian intensity profiles.
Conventional aberration (including chromatic aberration) correction methods of lens systems assume a uniform intensity light beam and attempt to minimize the total image blur from all rays over the whole entrance pupil. Such methods do not provide the best aberration correction for lens systems that are used with laser beams and, if a lens system is designed to be apochromatic for a uniform intensity light beam, do not assure that the beam waists of different wavelengths have the same location on the optical axis. The reasons for this are as follows:
A laser beam is much less intense at the margins than a uniform intensity light beam because the intensity drops off rapidly from the center of the beam. Thus, a conventional method that gives equal weight to all of the rays across the entrance pupil does not result in lens system that is well corrected for use with laser beams. In addition, the beam waist locations are not the same as paraxial foci location. Finally, conventional apochromatic lens systems are usually designed to work at an infinite conjugate (distant object), while lens systems for re-imaging beam waists operate at finite conjugates. Aberrations change with a shift of conjugates, so a lens system with a chromatic correction for an infinite conjugate would not generally work well at finite conjugates.
The term "chromatic correction" can mean that different wavelengths rays passing by the edge of the entrance pupil have nearly the same focus (as illustrated in FIGS. 1B and 2), or it can mean having the paraxial focus correction- i.e., having the same paraxial focus location for three or more wavelengths. An example of a ray intercept plot showing transverse ray aberration curves of an apochromatic lens system with paraxial focus correction is shown in FIG. 4. Since focus shift (represented on these aberration curves as a non-zero slope at the origin) is absent in these curves, this lens system has the same paraxial focus for the three wavelengths. FIG. 5 illustrates the paraxial focus shift as a function of wavelength for the same apochromatic lens system. This figure shows that the apochromatic lens system has five wavelengths focusing at the same paraxial image plane. This figure also shows that this apochromatic lens system provides a superb correction for wavelengths from 0.43 microns to 0.76 microns, the paraxial focus being within 10 microns across the whole wavelength range. While this would be an excellent conventional apochromatic lens system, it does not perform well when reimaging beam waists. This is because laser beam waists of different wavelengths across the visible spectrum are imaged by this apochromatic lens system at different image locations, as shown in FIG. 6. This is because, as stated above, the location of an imaged beam waist is not generally the same as the location of the paraxial focus.
U.S. Pat. Nos. 4,909,616 and 5,270,851 disclose lens systems for color correction of laser beams over relatively small wavelength ranges, such as found in monochromatic lasers during mode hopping. These lens systems are not corrected over the whole visible spectrum.
U.S. Pat. No. 5,694,251 discloses an F-theta lens system that is corrected for the lateral color aberration, but this an F-theta lens does not image beam waists of different wavelengths to a common location along the optical axis, which is more akin to axial color, the variation of focus with wavelength.
A collimating lens system corrected for chromatic variation in an infrared wavelength band is disclosed in U.S. Pat. No. 5,491,587. This lens system is not a finite conjugate lens system and does not image magnified multiple color beam waists to a common image location.